Quasiphantom categories on a family of surfaces isogenous to a higher product

Abstract

We construct exceptional collections of line bundles of maximal length 4 on $S=(C\times D)/G$ which is a surface isogenous to a higher product with $p_g=q=0$ where $G=G(32,27)$ is a finite group of order 32 having number 27 in the list of Magma library. From these exceptional collections, we obtain new examples of quasiphantom categories as their orthogonal complements.

arXiv comment18 pages; v2 reflects the revision made during the journal publication process

References in corpus (11)

• Hochschild homology and semiorthogonal decompositions
• Geometric Phantom Categories
• Determinantal Barlow surfaces and phantom categories
• On the derived category of the classical Godeaux surface
• Derived categories of Burniat surfaces and exceptional collections
• Exceptional collections of line bundles on the Beauville surface
• Height of exceptional collections and Hochschild cohomology of quasiphantom categories
• Semiorthogonal decompositions of derived categories of equivariant coherent sheaves
• Invariant stable bundles over modular curves X(p)
• A vanishing theorem on fake projective planes with enough automorphisms
• Exceptional collections on Dolgachev surfaces associated with degenerations

Cited by in corpus (1)

• Fano visitors, Fano dimension and orbifold Fano hosts